On sharp frame diagonalization

Abstract:

It was recently shown that if M = 1 ⊕ ··· ⊕ k ∈ Cn×n is a
Jordan matrix with k nontrivial Jordan blocks i, then M can be
frame diagonalized by embedding M into a diagonalizable matrix in
C(n+)×(n+) with = k. This naturally motivates a pursuit of the
best possible value of for which this is possible. Here, we use Lid-
skii’s Theorem on eigenvalue perturbations to construct diagonaliz-
ing frames for = k. := max{gmM(λ)|λ ∈ σ (M)}. Moreover, we verify that k. is sharp.